Discussiones Mathematicae Graph Theory 25(1-2) (2005)
95-102
DOI: https://doi.org/10.7151/dmgt.1264
COMBINATORIAL LEMMAS FOR POLYHEDRONS
Adam Idzik
Akademia Świetokrzyska |
Konstanty Junosza-Szaniawski
Warsaw University of Technology |
Abstract
We formulate general boundary conditions for a labelling to assure the existence of a balanced n-simplex in a triangulated polyhedron. Furthermore we prove a Knaster-Kuratowski-Mazurkiewicz type theorem for polyhedrons and generalize some theorems of Ichiishi and Idzik. We also formulate a necessary condition for a continuous function defined on a polyhedron to be an onto function.Keywords: KKM covering, labelling, primoid, pseudomanifold, simplicial complex, Sperner lemma.
2000 Mathematics Subject Classification: 05B30, 47H10, 52A20, 54H25.
References
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Recived 3 November 2003
Revised 21 March 2005
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